Pleased help?! Q1,3,4

Sampling from NII, (2) Do 1, 3 (nandc), 4 . 16: 0 2 = 1 Ha: 1 2 4 m = 5 1 =. 05 Develop best test ... 2. A single observation of a random variable having an exponential distribution is used to test the null hypothesis that the mean of the distribution is 0 = 2 against the alternative that it is 0 = 5. If the null hypothesis is accepted if and only if the observed value of the random variable is less than 3, find the probabilities of type I and type II errors. . . Let X1,....Xn denote a random sample from a normal N(0,25) distribution. Show that the best critical region for testing H. : 0 =5 vs. Ha : 0 =7 is C= {(x1,...,X) : x2 c]. Find n and c so that P(X Z C; H.)=.05 P( X 2 C; Ha)=.80 Find a UMP test, if one exists for testing Ho: H=2 versus Ha: